I've thought about this confusing behavior a lot, and to me it seems like the only sane way to fix it is by making trigger objectives disabled by default. First, let's look at the situation:

1. Set up a trigger objective:

   /scoreboard objectives add t trigger
   

2. Try to trigger it:

   /trigger t
   

   → "You cannot trigger this objective yet"

3. Enable the objective:

   /scoreboard players enable @p t
   

   → "Nothing changed, that trigger is already enabled"

4. Try another time to trigger the objective:

   /trigger t
   

   → This time, it works!

Now, why does it work in step 4, but not in step 2? Because step 3 initialized the objective, which seems to be WAI considering a bug related to exactly this behavior was fixed recently (MC-79255).

Note that this situation changed slightly from 1.12.2, in that enabling a trigger objective always succeeded in 1.12.2, even if it was already enabled.